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64m^{3}
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64m^{3}
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8m^{3}+36m^{2}n+54mn^{2}+27n^{3}+\left(2m-3n\right)^{3}+12m\left(4m^{2}-9n^{2}\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2m+3n\right)^{3}.
8m^{3}+36m^{2}n+54mn^{2}+27n^{3}+8m^{3}-36m^{2}n+54mn^{2}-27n^{3}+12m\left(4m^{2}-9n^{2}\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2m-3n\right)^{3}.
16m^{3}+36m^{2}n+54mn^{2}+27n^{3}-36m^{2}n+54mn^{2}-27n^{3}+12m\left(4m^{2}-9n^{2}\right)
Combine 8m^{3} and 8m^{3} to get 16m^{3}.
16m^{3}+54mn^{2}+27n^{3}+54mn^{2}-27n^{3}+12m\left(4m^{2}-9n^{2}\right)
Combine 36m^{2}n and -36m^{2}n to get 0.
16m^{3}+108mn^{2}+27n^{3}-27n^{3}+12m\left(4m^{2}-9n^{2}\right)
Combine 54mn^{2} and 54mn^{2} to get 108mn^{2}.
16m^{3}+108mn^{2}+12m\left(4m^{2}-9n^{2}\right)
Combine 27n^{3} and -27n^{3} to get 0.
16m^{3}+108mn^{2}+48m^{3}-108mn^{2}
Use the distributive property to multiply 12m by 4m^{2}-9n^{2}.
64m^{3}+108mn^{2}-108mn^{2}
Combine 16m^{3} and 48m^{3} to get 64m^{3}.
64m^{3}
Combine 108mn^{2} and -108mn^{2} to get 0.
8m^{3}+36m^{2}n+54mn^{2}+27n^{3}+\left(2m-3n\right)^{3}+12m\left(4m^{2}-9n^{2}\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2m+3n\right)^{3}.
8m^{3}+36m^{2}n+54mn^{2}+27n^{3}+8m^{3}-36m^{2}n+54mn^{2}-27n^{3}+12m\left(4m^{2}-9n^{2}\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2m-3n\right)^{3}.
16m^{3}+36m^{2}n+54mn^{2}+27n^{3}-36m^{2}n+54mn^{2}-27n^{3}+12m\left(4m^{2}-9n^{2}\right)
Combine 8m^{3} and 8m^{3} to get 16m^{3}.
16m^{3}+54mn^{2}+27n^{3}+54mn^{2}-27n^{3}+12m\left(4m^{2}-9n^{2}\right)
Combine 36m^{2}n and -36m^{2}n to get 0.
16m^{3}+108mn^{2}+27n^{3}-27n^{3}+12m\left(4m^{2}-9n^{2}\right)
Combine 54mn^{2} and 54mn^{2} to get 108mn^{2}.
16m^{3}+108mn^{2}+12m\left(4m^{2}-9n^{2}\right)
Combine 27n^{3} and -27n^{3} to get 0.
16m^{3}+108mn^{2}+48m^{3}-108mn^{2}
Use the distributive property to multiply 12m by 4m^{2}-9n^{2}.
64m^{3}+108mn^{2}-108mn^{2}
Combine 16m^{3} and 48m^{3} to get 64m^{3}.
64m^{3}
Combine 108mn^{2} and -108mn^{2} to get 0.
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